How to restore LR photos and catalog are on a time machine external drive

Because you mentioned a catalog, it sounds like you’re asking about Lightroom Classic. (Your question was posted in the forum for cloud-based Lightroom, which does not use catalogs.)

You asked how to make “the time machine hard drive to become main drive for my LR.” But it isn’t possible to work directly from a Time Machine backup, because it’s in a special backup format and Apple also wants to keep backups safe from corruption. The way Apple intends Time Machine to be used is that if you need to use something that is only in the backup, you must restore it to from Time Machine to your Mac. That means copying the backup files you need from the Time Machine backup to your Mac storage. Then you can reconnect those restored folders in Lightroom Classic.

For example, in this case, if you bought a replacement hard drive, now you want to restore both your Lightroom Classic catalog folder and all folders containing original photos back to your new replacement hard drive. You could use Time Machine to restore the entire external hard drive in one step. Here is an article about how to do that.

How to restore items for an external drive that’s backed up using Time Machine (Macworld magazine)

You can also manually browse a Time Machine backup on the desktop when it’s connected, so you could also find the external hard drive’s backup in there and drag-copy the whole thing to the new external hard drive.